Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 7 - Section 7.5 - Systems of Inequalities - Exercise Set - Page 866: 118


a. $6.8$ million. b. $18.4$ million, underestimates by 0.4 million. c. $25.1$ million.

Work Step by Step

a. In 1970, we have $t=0$ and $f(0)=\frac{25.1}{1+2.7e^{0}}=\frac{25.1}{3.7}\approx6.8$ million. b. In 2010, we have $t=2010-1970=40$ and $f(40)=\frac{25.1}{1+2.7e^{-0.05(40)}}\approx18.4$ million. Compare to 18.8 million, the model underestimates the value by 0.4 million. c. When $t\to\infty$, we have $f\to 25.1$ million which gives the limiting size of the population.
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